Spacing between Atomic Lattice Planes in X-ray Diffraction Calculator

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✖Order of reflection, waves reflected through an angle corresponding to n=1 is said to be in the first order of reflection; the angle corresponding to n = 2 is the second order, and so on.ⓘ Order of Reflection [n_order]			+10% -10%
✖The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray.ⓘ Wavelength of X-ray [λ_X-ray]			+10% -10%
✖Angle b/w Incident and Reflected X-Ray is the angle between the wave vector of the incident plane wave.ⓘ Angle b/w Incident and Reflected X-Ray [θ]			+10% -10%

✖Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.ⓘ Spacing between Atomic Lattice Planes in X-ray Diffraction [d]

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Formula

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Spacing between Atomic Lattice Planes in X-ray Diffraction

Formula

`"d" = ("n"_{"order"}*"λ"_{"X-ray"})/(2*sin("θ"))`

Example

`"0.9nm"=("2"*"0.45nm")/(2*sin("30°"))`

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Spacing between Atomic Lattice Planes in X-ray Diffraction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray))
d = (n_order*λ_X-ray)/(2*sin(θ))
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Interplanar Spacing - (Measured in Meter) - Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.
Order of Reflection - Order of reflection, waves reflected through an angle corresponding to n=1 is said to be in the first order of reflection; the angle corresponding to n = 2 is the second order, and so on.
Wavelength of X-ray - (Measured in Meter) - The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray.
Angle b/w Incident and Reflected X-Ray - (Measured in Radian) - Angle b/w Incident and Reflected X-Ray is the angle between the wave vector of the incident plane wave.

STEP 1: Convert Input(s) to Base Unit

Order of Reflection: 2 --> No Conversion Required
Wavelength of X-ray: 0.45 Nanometer --> 4.5E-10 Meter (Check conversion here)
Angle b/w Incident and Reflected X-Ray: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = (n_order*λ_X-ray)/(2*sin(θ)) --> (2*4.5E-10)/(2*sin(0.5235987755982))

Evaluating ... ...

d = 9E-10

STEP 3: Convert Result to Output's Unit

9E-10 Meter -->0.9 Nanometer (Check conversion here)

FINAL ANSWER

0.9 Nanometer <-- Interplanar Spacing

(Calculation completed in 00.020 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 10+ Atom Calculators

Angle between Incident Ray and Scattering Planes in X-ray Diffraction

Go Angle b/w Incident and Reflected X-Ray = asin((Order of Reflection*Wavelength of X-ray)/(2*Interplanar Spacing))

Spacing between Atomic Lattice Planes in X-ray Diffraction

Go Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray))

Wavelength in X-ray Diffraction

Go Wavelength of X-ray = (2*Interplanar Spacing*sin(Angle b/w Incident and Reflected X-Ray))/Order of Reflection

Wavelength of Emitted Radiation for Transition between States

Go Wavelength = [Rydberg]*Atomic Number^2*(1/Energy State n1^2-1/Energy State n2^2)

Quantization of Angular Momentum

Go Quantization of Angular Momentum = (Quantum Number*Plancks Constant)/(2*pi)

Moseley's Law

Go Moseley Law = Constant A*(Atomic Weight-Constant B)

Energy in Nth Bohr's Orbit

Go Energy in nth Bohr's Unit = -13.6*(Atomic Number^2)/(Number of Level in Orbit^2)

Radius of Nth Bohr's Orbit

Go Radius of nth Orbit = (Quantum Number^2*0.529*10^(-10))/Atomic Number

Minimum Wavelength in X-ray Spectrum

Go Wavelength = Plancks Constant*3*10^8/(1.60217662*10^-19*Voltage)

Photon Energy in State Transition

Go Energy of Photon = Plancks Constant*Frequency of Photon

Spacing between Atomic Lattice Planes in X-ray Diffraction Formula

Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray))
d = (n_order*λ_X-ray)/(2*sin(θ))

What is Bragg's law of X ray diffraction?

Bragg's Law was introduced by Sir W.H. Bragg and his son Sir W.L. Bragg. The law states that when the x-ray is incident onto a crystal surface, its angle of incidence, θ, will reflect back with a same angle of scattering.

How to Calculate Spacing between Atomic Lattice Planes in X-ray Diffraction?

Spacing between Atomic Lattice Planes in X-ray Diffraction calculator uses Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray)) to calculate the Interplanar Spacing, The Spacing between Atomic Lattice Planes in X-ray Diffraction formula is defined as the distance between the atomic layers. Interplanar Spacing is denoted by d symbol.

How to calculate Spacing between Atomic Lattice Planes in X-ray Diffraction using this online calculator? To use this online calculator for Spacing between Atomic Lattice Planes in X-ray Diffraction, enter Order of Reflection (n_order), Wavelength of X-ray (λ_X-ray) & Angle b/w Incident and Reflected X-Ray (θ) and hit the calculate button. Here is how the Spacing between Atomic Lattice Planes in X-ray Diffraction calculation can be explained with given input values -> 9E+8 = (2*4.5E-10)/(2*sin(0.5235987755982)).

FAQ

What is Spacing between Atomic Lattice Planes in X-ray Diffraction?

The Spacing between Atomic Lattice Planes in X-ray Diffraction formula is defined as the distance between the atomic layers and is represented as d = (n_order*λ_X-ray)/(2*sin(θ)) or Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray)). Order of reflection, waves reflected through an angle corresponding to n=1 is said to be in the first order of reflection; the angle corresponding to n = 2 is the second order, and so on, The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray & Angle b/w Incident and Reflected X-Ray is the angle between the wave vector of the incident plane wave.

How to calculate Spacing between Atomic Lattice Planes in X-ray Diffraction?

The Spacing between Atomic Lattice Planes in X-ray Diffraction formula is defined as the distance between the atomic layers is calculated using Interplanar Spacing = (Order of Reflection*Wavelength of X-ray)/(2*sin(Angle b/w Incident and Reflected X-Ray)). To calculate Spacing between Atomic Lattice Planes in X-ray Diffraction, you need Order of Reflection (n_order), Wavelength of X-ray (λ_X-ray) & Angle b/w Incident and Reflected X-Ray (θ). With our tool, you need to enter the respective value for Order of Reflection, Wavelength of X-ray & Angle b/w Incident and Reflected X-Ray and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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